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A Treatise On The Differential Geometry Of Curves And Surfaces
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Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1909 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Book Synopsis Treatise On the Differential Geometry of Curves and Surfaces by : Eisenhart Luther Pfahler
Download or read book Treatise On the Differential Geometry of Curves and Surfaces written by Eisenhart Luther Pfahler and published by . This book was released on 1901 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1965 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1960 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces (Classic Reprint) by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces (Classic Reprint) written by Luther Pfahler Eisenhart and published by Forgotten Books. This book was released on 2017-09-18 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Treatise on the Differential Geometry of Curves and Surfaces The remainder of the book may be divided into three parts. The first, consisting of Chapters II - VI, deals with the geometry of a sur face ih the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equa tions. To a large extent the method is that of Gauss, by which the properties of a surface are derived from the discussion of two quad ratio differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of differential equa tions and boundary conditions the reader must consult the treatises which deal particularly with these subjects. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces (1909) by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces (1909) written by Luther Pfahler Eisenhart and published by Literary Licensing, LLC. This book was released on 2014-08-07 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is A New Release Of The Original 1909 Edition.
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by Forgotten Books. This book was released on 2015-06-15 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Treatise on the Differential Geometry of Curves and Surfaces This book is a development from courses which I have given in Princeton for a number of years. During this time I have come to feel that more would be accomplished by my students if they had an introductory treatise written in English and otherwise adapted to the use of men beginning their graduate work. Chapter I is devoted to the theory of twisted curves, the method in general being that which is usually followed in discussions of this subject. But in addition I have introduced the idea of moving axes, and have derived the formulas pertaining thereto from the previously obtained Frenet-Serret formulas. In this way the student is made familiar with a method which is similar to that used by Darboux in the first volume of his Leçons, and to that of Cesaro in his Geometria Intrinseca. This method is not only of great advantage in the treatment of certain topics and in the solution of problems, but it is valuable in developing geometrical thinking. The remainder of the book may be divided into three parts. The first, consisting of Chapters II-VI, deals with the geometry of a surface in the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equations. To a large extent the method is that of Gauss, by which the properties of a surface are derived from the discussion of two quadratic differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of differential equations and boundary conditions the reader must consult the treatises which deal particularly with these subjects. In Chapters VII and VIII the theory previously developed is applied to several groups of surfaces, such as the quadrics, ruled surfaces, minimal surfaces, surfaces of constant total curvature, and surfaces with plane and spherical lines of curvature. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis Differential Geometry of Curves and Surfaces by : Manfredo P. do Carmo
Download or read book Differential Geometry of Curves and Surfaces written by Manfredo P. do Carmo and published by Courier Dover Publications. This book was released on 2016-12-14 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
Book Synopsis Introduction to Differential Geometry of Space Curves and Surfaces by : Taha Sochi
Download or read book Introduction to Differential Geometry of Space Curves and Surfaces written by Taha Sochi and published by Lulu.com. This book was released on with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Victor Andreevich Toponogov Publisher :Springer Science & Business Media ISBN 13 :0817644024 Total Pages :215 pages Book Rating :4.8/5 (176 download)
Book Synopsis Differential Geometry of Curves and Surfaces by : Victor Andreevich Toponogov
Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Book Synopsis Differential Geometry by : Wolfgang Kühnel
Download or read book Differential Geometry written by Wolfgang Kühnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Book Synopsis Differential Geometry of Curves and Surfaces by : Thomas F. Banchoff
Download or read book Differential Geometry of Curves and Surfaces written by Thomas F. Banchoff and published by CRC Press. This book was released on 2010-03-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Book Synopsis Modern Differential Geometry of Curves and Surfaces with Mathematica by : Elsa Abbena
Download or read book Modern Differential Geometry of Curves and Surfaces with Mathematica written by Elsa Abbena and published by CRC Press. This book was released on 2017-09-06 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
Book Synopsis Differential Geometry of Curves and Surfaces by : Masaaki Umehara
Download or read book Differential Geometry of Curves and Surfaces written by Masaaki Umehara and published by World Scientific Publishing Company. This book was released on 2017-05-12 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well. Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates. Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities. In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field. Request Inspection Copy
Book Synopsis Projective differential geometry of curves and ruled surfaces by : Ernest Julius Wilczynski
Download or read book Projective differential geometry of curves and ruled surfaces written by Ernest Julius Wilczynski and published by . This book was released on 1906 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry of Curves and Surfaces by : Manfredo Perdigão do Carmo
Download or read book Differential Geometry of Curves and Surfaces written by Manfredo Perdigão do Carmo and published by Prentice Hall. This book was released on 1976 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers local as well as global differential geometry of curves and surfaces.
Book Synopsis Differential Geometry of Curves and Surfaces by : Thomas F. Banchoff
Download or read book Differential Geometry of Curves and Surfaces written by Thomas F. Banchoff and published by CRC Press. This book was released on 2022-08-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Third edition has been made more accessible by offering more graduated exercise sets. Also, Maple applets replace the Java used in the previous two editions. There are other books with this title, yet none offer integrated technology to assist students in visualizing the concepts. The use of Maple to build in a visual element, often in three dimensions, creates an opportunity for readers, instructors, and students will find compelling.
